Title: Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups Show Chinese title

Title: 非对易的 (A)dS 和闵可夫斯基时空来自量子洛伦兹子群

Abstract: The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists three classes of such $r$-matrices, one of them being a novel two-parametric one. The (A)dS and Minkowskian Poisson homogeneous spaces corresponding to these three deformations are explicitly constructed in both local and ambient coordinates. Their quantization is performed, thus giving rise to the associated noncommutative spacetimes, that in the Minkowski case are naturally expressed in terms of quantum null-plane coordinates, and they are always defined by homogeneous quadratic algebras. Finally, non-relativistic and ultra-relativistic limits giving rise to novel Newtonian and Carrollian noncommutative spacetimes are also presented. Show Chinese abstract

Abstract: 对生成(3+1)维(A)dS和庞加莱群量子变形的经典$r$-矩阵的完整分类进行了阐述，使得其洛伦兹部分是一个量子子群。 发现存在三类这样的$r$-矩阵，其中一类是新颖的双参数矩阵。 对应于这三种变形的(A)dS和闵可夫斯基泊松齐性空间在局部坐标和环境坐标中都被显式构造出来。 它们的量子化也被完成，从而产生了相关的非对易时空，其中在闵可夫斯基情况下，它们自然地用量子零平面坐标来表达，并且总是由齐次二次代数定义。 最后，还给出了产生新颖牛顿和卡罗尔非对易时空的非相对论和极端相对论极限。